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- Erik D. Demaine, Martin L. Demaine, +4 authors Diane L. Souvaine
- Natural Computing
- 2007

We introduce staged self-assembly of Wang tiles, where tiles can be added dynamically in sequence and where intermediate constructions can be stored for later mixing. This model and its various constraints and performance measures are motivated by a practical nanofabrication scenario through protein-based bioengineering. Staging allows us to break through… (More)

- Erik D. Demaine, Martin L. Demaine
- Graphs and Combinatorics
- 2007

- Zachary Abel, Nadia Benbernou, +5 authors Robert T. Schweller
- SODA
- 2010

We introduce the problem of <i>shape replication</i> in the Wang tile self-assembly model. Given an input shape, we consider the problem of designing a self-assembly system which will replicate that shape into either a specific number of copies, or an unbounded number of copies. Motivated by practical DNA implementations of Wang tiles, we consider a model… (More)

- Sarah Cannon, Erik D. Demaine, +5 authors Andrew Winslow
- ArXiv
- 2012

We study the difference between the standard seeded model of tile self-assembly, and the “seedless” two-handed model of tile self-assembly. Most of our results suggest that the two-handed model is more powerful. In particular, we show how to simulate any seeded system with a two-handed system that is essentially just a constant factor larger. We exhibit… (More)

- Erik D. Demaine, Martin L. Demaine, Joseph O'Rourke
- CCCG
- 2000

We prove that two pushing-blocks puzzles are intractable in 2D. One of our constructions improves an earlier result that established intractability in 3D [OS99] for a puzzle inspired by the game PushPush. The second construction answers a question we raised in [DDO00] for a variant we call Push-1. Both puzzles consist of unit square blocks on an integer… (More)

- Esther M. Arkin, Michael A. Bender, +4 authors Steven Skiena
- Comput. Geom.
- 2001

We explore the following problem: given a collection of creases on a piece of paper, each assigned a folding direction of mountain or valley, is there a flat folding by a sequence of simple folds? There are several models of simple folds; the simplest one-layer simple fold rotates a portion of paper about a crease in the paper by ±180◦. We first consider… (More)

We study a popular puzzle game known variously as Clickomania and Same Game. Basically, a rectangular grid of blocks is initially colored with some number of colors, and the player repeatedly removes a chosen connected monochromatic group of at least two square blocks, and any blocks above it fall down. We show that one-column puzzles can be solved, i.e.,… (More)

- Erik D. Demaine, Martin L. Demaine, Craig S. Kaplan
- CCCG
- 2000

We introduce and characterize a new class of polygons that models wood, stone, glass, and ceramic shapes that can be cut with a table saw, lapidary trim saw, or other circular saw. In this model, a circular saw is a line segment (in projection) that can move freely in empty space, but can only cut straight into a portion of material. Once a region of… (More)

- Erik D. Demaine, Martin L. Demaine, Rudolf Fleischer
- Theor. Comput. Sci.
- 2002

Clobber is a new two-player board game. In this paper, we introduce the 1-player variant Solitaire Clobber where the goal is to remove as many stones as possible from the board by alternating white and black moves. We show that a checkerboard configuration on a single row (or single column) can be reduced to about n/4 stones. For boards with at least two… (More)

- Therese C. Biedl, Erik D. Demaine, +5 authors Sue Whitesides
- CCCG
- 1998

In this paper, we study unfoldings of orthogonal polyhedra. More precisely, we deene two special classes of orthogonal polyhedra, orthostacks and orthotubes, and show how to generate unfoldings by cutting faces, such that the resulting surfaces can be attened into a single connected polygon.